1 / 30

Starting Out with C++ Early Objects Ninth Edition

Chapter 9: Searching, Sorting, and Algorithm Analysis. Starting Out with C++ Early Objects Ninth Edition by Tony Gaddis, Judy Walters, and Godfrey Muganda. Topics. 9.1 Introduction to Search Algorithms 9.2 Searching an Array of Objects 9.3 Introduction to Sorting Algorithms

joeedwards
Download Presentation

Starting Out with C++ Early Objects Ninth Edition

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Chapter 9: Searching, Sorting, and Algorithm Analysis Starting Out with C++ Early Objects Ninth Edition by Tony Gaddis, Judy Walters, and Godfrey Muganda

  2. Topics 9.1 Introduction to Search Algorithms 9.2 Searching an Array of Objects 9.3 Introduction to Sorting Algorithms 9.4 Sorting an Array of Objects 9.5 Sorting and Searching Vectors 9.6 Introduction to Analysis of Algorithms

  3. 9.1 Introduction to Search Algorithms • Search: to locate a specific item in a list (array, vector, etc.) of information • Two algorithms (methods) considered here: • Linear search (also called Sequential Search) • Binary search

  4. Linear Search Algorithm Set found to false Set position to –1 Set index to 0 While index < number of elts and found is false If list [index] is equal to search value found = true position = index End If Add 1 to index End While Return position

  5. Linear Search Example • Array numlist contains • Searching for the the value 11, linear search examines 17, 23, 5, and 11 • Searching for the the value 7, linear search examines 17, 23, 5, 11, 2, 29, and 3

  6. Linear Search Tradeoffs • Benefits • Easy algorithm to understand and to implement • Elements in array can be in any order • Disadvantage • Inefficient (slow): for array of N elements, it examines N/2 elements on average for a value that is found in the array, N elements for a value that is not in the array

  7. Binary Search Algorithm Binary search requires that the array is in order. • Examine the value of the middle element • If the middle element has the desired value, done. Otherwise, determine which half of the array may have the desired value. Continue working with this portion of the array. • Repeat steps 1 and 2 until either the element with the desired value is found or there are no more elements to examine.

  8. Binary Search Example • Array numlist2 contains • Searching for the the value 11, binary search examines 11 and stops • Searching for the the value 7, binary search examines 11, 3, 5, then stops

  9. Binary Search Tradeoffs • Benefit • It is much more efficient than linear search. For an array of N elements, the number of comparisons is the smallest integer x such that . When N = 20,000, x is 15. • However, • It requires that the array elements be in order

  10. 9.2 Searching an Array of Objects Search algorithms are not limited to arrays of integers When searching an array of objects or structures, the value being searched for is a member of an object or structure, not the entire object or structure Member in object/structure: key field Value used in search: search key

  11. 9.3 Introduction to Sorting Algorithms • Sort: arrange values into an order • Alphabetical • Ascending (smallest to largest) numeric • Descending (largest to smallest) numeric • Two algorithms considered here • Bubble sort • Selection sort

  12. Bubble Sort Algorithm • Compare 1st two elements and exchange them if they are out of order. • Move down one element and compare 2nd and 3rd elements. Exchange if necessary. Continue until the end of the array. • Pass through the array again, repeating the process and exchanging as necessary. • Repeat until a pass is made with no exchanges.

  13. 17 17 17 23 5 5 5 23 11 11 11 23 Bubble Sort Example Array numlist3 contains Compare values 17 and 23. They are in order, so no exchange is needed. Compare values 23 and 5. Exchange them. Compare values 23 and 11. Exchange them. This is the end of the first pass.

  14. 17 5 5 5 17 11 11 11 17 23 23 23 Bubble Sort Example, Continued The second pass starts with the array from pass one Compare values 17 and 5. Exchange them. Compare 17 and 11. Exchange them. Compare 17 and 23. No exchange is needed. This is the end of the second pass.

  15. 5 11 17 23 Bubble Sort Example, Continued The third pass starts with the array from pass two Compare values 5 and 11. No exchange is needed. Compare values 11 and 17. No exchange is needed. Compare values 17 and 23. No exchange is needed. Since no exchanges were made, the array is in order.

  16. Bubble Sort Tradeoffs • Benefit • It is easy to understand and to implement • Disadvantage • It is inefficient due to the number of exchanges. This makes it slow for large arrays

  17. Selection Sort Algorithm • Locate the smallest element in the array and exchange it with the element in position 0. • Locate the next smallest element in the array and exchange it with element in position 1. • Continue until all of the elements are in order.

  18. Selection Sort Example Now in order Array numlistcontains The smallest element is 2. Exchange 2 with the element at subscript 0.

  19. Selection Sort Example, Continued The next smallest element is 3. Exchange 3 with the element at subscript 1. The next smallest element is 11. Exchange 11 with the element at subscript 2.

  20. Sorting Considerations Selection Sort is considered more efficient than Bubble Sort, due to the fewer number of exchanges that occur. Another efficient sorting algorithm will be seen in Chapter 14.

  21. 9.4 Sorting an Array of Objects As with searching, arrays to be sorted can contain objects or structures The key field determines how the structures or objects will be ordered When exchanging the contents of array elements, entire structures or objects must be exchanged, not just the key fields in the structures or objects

  22. 9.5 Sorting and Searching Vectors • Sorting and searching algorithms can be applied to vectors as well as to arrays • You need slight modifications to functions to use vector arguments • vector <type> & used in prototype • There is no need to indicate the vector size, as functions can use the vector’s size member function

  23. 9.6 Introduction to Analysis of Algorithms • Given two algorithms to solve a problem, what makes one better than the other? • Efficiency of an algorithm is measured by • space (computer memory used) • time (how long to execute the algorithm) • Analysis of algorithms is a more effective way to find efficiency than by using empirical data

  24. Analysis of Algorithms: Terminology Computational Problem: a problem solved by an algorithm Instance of the Problem: a specific problem that is solved by the algorithm Size of an Instance: the amount of memory needed to hold the data for the specific problem

  25. Analysis of Algorithms: More Terminology • Basic step: an operation in the algorithm that executes in a constant amount of time • Examples of basic steps: • exchange the contents of two variables • compare two values • Non-example of a basic step: • find the largest element in an array

  26. Analysis of Algorithms: Terminology Complexity of an algorithm: the number of basic steps required to execute the algorithm for an input of size N (N = number of input values) Worst-case complexity of an algorithm: the number of basic steps for input of size N that requires the most work Average case complexity function: the complexity for typical, average inputs of size N

  27. Complexity Example Find the largest value in array A of size n • biggest = A[0] • indx = 0 • while (indx < n) do • if (A[n] > biggest) • then • biggest = A[n] • end if • end while Analysis: Lines 1 and 2 execute once. The test in line 3 executes n times. The test in line 4 executes n times. The assignment in line 6 executes at most n times. Due to lines 3 and 4, the algorithm requires execution time proportional to n.

  28. Comparison of Algorithmic Complexity Given algorithms F and G with complexity functions f(n) and g(n) for input of size n • If the ratio approaches a constant value as n gets large, F and G have equivalent efficiency • If the ratio gets larger as n gets large, algorithm G is more efficient than algorithm F • If the ratio approaches 0 as n gets large, algorithm F is more efficient than algorithm G

  29. "Big O" Notation Function f(n) is O(g(n)) (“f is big O of g") for some mathematical function g(n) if the ratio approaches a positive constant as n gets large O(g(n)) defines a complexity class for the function f(n) and for the algorithm F Increasing complexity classes means faster rate of growth and less efficient algorithms

  30. Chapter 9: Searching, Sorting, and Algorithm Analysis Starting Out with C++ Early Objects Ninth Edition by Tony Gaddis, Judy Walters, and Godfrey Muganda

More Related